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A077116
n^3 - A065733(n).
23
0, 0, 4, 2, 0, 4, 20, 19, 28, 0, 39, 35, 47, 81, 40, 11, 0, 13, 56, 135, 79, 45, 39, 67, 135, 0, 152, 83, 48, 53, 104, 207, 7, 216, 100, 26, 0, 28, 116, 270, 496, 277, 104, 546, 503, 524, 615, 139, 368, 0, 391, 155, 732, 652, 648, 726, 55, 293, 631, 170, 704
OFFSET
0,3
COMMENTS
a(n) = 0 for n = m^2. - Zak Seidov, May 11 2007
It has been asked whether some primes do not occur in this sequence. It seems indeed that primes 3, 5, 17, 23, 29, 31, 37, 41, 43, 59, 61,... do not occur, primes 2, 7, 11, 13, 19, 47, 53, 67, 79, 83,... do. For further investigations, see A087285 = the range of this sequence, and also the related sequences A229618 = range of A181138, and A165288. - M. F. Hasler, Sep 26 2013 and Oct 05 2013
FORMULA
a(n) = A154333(n) unless n is a square or, equivalently, a(n)=0. - M. F. Hasler, Oct 05 2013
a(n) = A053186(n^3). - R. J. Mathar, Jul 12 2016
EXAMPLE
A065733(10) = 961 = 31^2 is the largest square less than or equal to 10^3 = 1000, therefore a(10) = 1000 - 961 = 39.
MAPLE
A077116 := proc(n)
A053186(n^3) ;
end proc: # R. J. Mathar, Jul 12 2016
MATHEMATICA
Table[c = n^3; c - Floor[Sqrt[c]]^2, {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 02 2011 *)
PROG
(PARI) A077116(n)=n^3-sqrtint(n^3)^2 \\ - M. F. Hasler, Sep 26 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 29 2002
STATUS
approved